Boundary contraction solution of the Neumann and mixed boundary value problems of the Laplace equation

The boundary contraction method is generalized in such a way that it is applicable to the Neumann and mixed boundary value problems over regions of irregular shape. Various variants of mixed boundary value problems can be solved numerically in a unified way with mesh points fewer than those required of ADI and SOR. The method is not iterative and therefore does not require the positive definiteness of eigenvalues which is the necessary condition of the stability of ADI and SOR. The method is also applicable to exterior problems. Thus the applicability of the contraction method to problems of practical importance is substantially improved.     

Brightening of triplet dark excitons by atomic hydrogen adsorption in single-walled carbon nanotubes observed by photoluminescence spectroscopy

Adsorption and desorption of atomic hydrogen on single-walled carbon nanotubes were observed by photoluminescence spectroscopy. A satellite peak appeared at the lower energy side of the E11 photoluminescence emission peak after exposure to atomic hydrogen and then disappeared after annealing at 300?°C in vacuum. The energy difference between the satellite peak and E11 peak was 40-80 meV, depending on the tube diameter. The satellite peak was attributed to the triplet dark exciton that became optically active because of the effectively enhanced spin-orbit interaction induced by adsorbed hydrogen atoms.     

Counter-examples for refinement of conjectures and proofs in primary school mathematics

The purpose of this study is to explore how primary school students reexamine their conjectures and proofs when they confront counter-examples to the conjectures they have proved. In the case study, a pair of Japanese fifth graders thought that they had proved their primitive conjecture with manipulative objects (that is, they constructed an action proof), and then the author presented a counter-example to them. Confronting the counter-example functioned as a driving force for them to refine their conjectures and proofs. They understood the reason why their conjecture was false through their analysis of its proof and therefore could modify their primitive conjecture. They also identified the part of the proof which was applicable to the counter-example. This identification and their action proof were essential for their invention of a more comprehensive conjecture.     

Rethinking the discovery function of proof within the context of proofs and refutations

Proof and proving are important components of school mathematics and have multiple functions in mathematical practice. Among these functions of proof, this paper focuses on the discovery function that refers to invention of a new statement or conjecture by reflecting on or utilizing a constructed proof. Based on two cases in which eighth and ninth graders engaged in proofs and refutations, we demonstrate that facing a counterexample of a primitive statement can become a starting point of students’ activity for discovery, and that a proof of the primitive statement can function as a useful tool for inventing a new conjecture that holds for the counterexample. An implication for developing tasks by which students can experience this discovery function is mentioned.     

Direct construction of bicyclic heterocycles by palladium-catalyzed domino cyclization of propargyl bromides

The palladium-catalyzed domino cyclization of propargyl bromides having two nucleophilic functional groups is described. Treatment of 1,7-diamino-5-bromohept-3-yne derivatives with catalytic Pd(PPh3)4 in the presence of NaH in MeOH gives the 2,7-diazabicyclo[4.3.0]non-5-enes in good yields. Interestingly, the regioselectivity of the reaction is completely controlled by the relative reactivity of the amine functional groups, irrespective of the position of the nucleophiles. The malonate derivative also undergoes domino cyclization to produce a hexahydroindole derivative.     

Fluorescence determination of N-acetylaspartic acid in the rat cerebrum homogenate using high-performance liquid chromatography with pre-column fluorescence derivatization

N-acetyl-L-aspartic acid (NAA) is an endogenous compound, and its brain concentration is suggested to be altered in neurological disorders. In the present study, a fluorescence determination method for NAA was developed by employing reversed-phase high-performance liquid chromatography (HPLC) with pre-column fluorescence derivatization using 4-N,N-dimethylaminosulfonyl-7-N-(2-aminoethyl)amino-2,1,3-benzoxadiazole (DBD-ED). Using methylsuccinic acid as the internal standard, a linear calibration curve for NAA was constructed in the range 125-1000 microM (n=3). The detection limit on the column was approximately 5.0 fmol (signal-to-noise ratio 3). The proposed HPLC method was applied to determine NAA in the rat cerebrum homogenate. Cerebrum NAA was successfully determined using 10 microL of the homogenate, and the validation data for the proposed HPLC method demonstrated satisfactory results. Intra- and inter-day precision and accuracy were within 1.1-7.0 and -8.1-6.3%, respectively. The concentration of NAA in the male rat cerebrum (13 weeks old) was 84+/-4.6 micromol/mg protein (n=3).     

Diffusion of metal complexes inside of silica-surfactant nanochannels within a porous alumina membrane

The present paper describes diffusivities of a series of metal complexes inside of silica-surfactant nanochannels (channel diameter = 3.4 nm), which were formed within a porous alumina membrane by a surfactant-templated method using cetyltrimethylammonium bromide (CTAB) as a template surfactant. The metal complexes used in this study were Fe(CN)6(3-), Ru(NH3)6(3-), ferrocenecarboxylic acid (Fc-COO-), (ferrocenylmethyl)-trimethylammonium (Fc-NMe3+), N,N-(dimethylamminomethyl)ferrocene (Fc-NMe2), and ferrocene methanol (Fc-OH). Apparent diffusion coefficients of these metal complexes were estimated by measuring their mass transports through the silica-surfactant nanochannels. The estimated apparent diffusion coefficients were on the order of 10(-11) cm2 s(-1) for Fe(CN)6(3-) and Ru(NH3)6(3-), and these values were five orders of magnitude smaller than those in a bulk aqueous solution. For the ferrocene derivatives, the apparent diffusion coefficients of charged ferrocene derivatives are almost the same (5.3 x 10(-11) cm2 s(-1) for Fc-COO- and 5.4 x 10(-11) cm2 s(-1) for Fc-NMe3+), whereas neutral ferrocene derivatives (Fc-NMe2 and Fc-OH) show faster diffusion than the charged species. In addition, the apparent diffusion coefficient of Fc-NMe2 (27 x 10(-11) cm2 s(-1)) was about three times larger than that of Fc-OH (10 x 10-11 cm2 s(-1)). The difference in these diffusion coefficients is discussed by considering the mesostructure of the silica-surfactant nanochannels, that is, an ionic interface with cationic head groups of CTA and their counteranions, a hydrophobic interior of the micellar phase, and a silica framework. As a result, it is inferred that the slow diffusivities of the charged metal complexes are due to the electrostatic interaction between the charged species and the ionic interface, whereas less interaction between neutral ferrocenes and the ionic interface causes distribution of metal complexes into the hydrophobic micellar phase, which is a less viscous medium compared to the ionic interface, resulting in the faster diffusivities of the neutral species.     

Nonlinear optical detection of proteins based on localized surface plasmons in surface immobilized gold nanospheres

A new nonlinear optical method is presented to detect proteins binding to a gold surface without using fluorescent-dye labeling. After exposure of the protein-binding surface to a gold nanosphere solution, the nanospheres are immobilized above a gold surface with a nanogap supported by the protein. The gold nanospheres immobilized on the gold surface show strong localized surface plasmon (LSP) resonance, and the formation of this structure results in a marked increase in the optical second harmonic (SH) activity of the gold surface arising from a large enhancement of the electric field localized adjacent to the nanospheres on the LSP resonance. The SH image, therefore, gives a high contrast ratio, 7.0:1, of protein-binding spots to control spots. The contrast ratio is much greater than those obtained by linear reflectivity imaging.